13 Nov 2020 |
VIVIT | The etymology of "iff" is as a contraction of "if and only if". It's used to express logical equivalence: "A number is prime iff it is a natural number with two and only two distinct natural number factors." | 21:10:40 |
VIVIT | If you said "A number is prime if it is a natural number with two and only two distinct natural-number factors", then that would imply that it's possible for there to be a prime number with more than two natural-number factors. | 21:14:04 |
VIVIT | You said, "All numbers that are this way are prime." You didn't say, "All prime numbers are this way." | 21:14:49 |
Cur_固嚛訥 | Cringe if that happens. | 21:15:28 |
Cur_固嚛訥 | Mark Twain's terrible prophesy. | 21:15:52 |
Cur_固嚛訥 | Per chance, do you want experiment and challenge the prose of my word "ob" more? | 21:17:56 |
Cur_固嚛訥 | * Per chance, do you want t experiment and challenge the prose of my word "ob" more? | 21:18:31 |
Cur_固嚛訥 | * Per chance, do you want to experiment and challenge the prose of my word "ob" more? | 21:18:37 |
Cur_固嚛訥 | Otherwise, I do want to elaborate my theories regarding primordial Siberia. | 21:20:03 |
VIVIT | And if you said "A number is prime only if it is a natural number with two and only two distinct natural-number factors," then that would imply that there might be numbers that have exactly two natural-number factors, but aren't prime. You said "All prime numbers are this way," but never not, "Only prime numbers are this way." | 21:20:21 |
VIVIT | * And if you said "A number is prime only if it is a natural number with two and only two distinct natural-number factors," then that would imply that there might be numbers that have exactly two natural-number factors, but aren't prime. You said "All prime numbers are this way," but not, "Only prime numbers are this way." | 21:20:29 |
VIVIT | The only way for you to express both is to use the phrase "if and only if", or its contraction, "iff". | 21:20:49 |
Cur_固嚛訥 | Though that might appear like a typo, the message would come quite clear in verbal communication. | 21:23:27 |
Cur_固嚛訥 | Why is seven the loneliest number? | 21:28:45 |
Cur_固嚛訥 | Interrupt me if you want to make a guess. | 21:29:18 |
Cur_固嚛訥 | Seven turns out the loneliest number, because
if you organize the numbers from one to ten
where each group factors into the same
prime numbers seven will always
be the number which makes
one group different from
the other. | 21:32:56 |
Cur_固嚛訥 | Redacted or Malformed Event | 21:35:51 |
Cur_固嚛訥 | Group: 6 3 8 5
Group: 9 4 2 10 | 21:42:19 |
Cur_固嚛訥 | * What makes seven the loneliest number? | 21:45:45 |
VIVIT | Hold on, what? | 21:53:36 |
VIVIT | Seven is the loneliest number because if you orgaize the natural numbers from 1 to 10 into set such that... what next? | 21:56:35 |
VIVIT | What is true of each set? | 21:56:41 |
VIVIT | What do you mean by "each group factors into the same prime numbers"? | 22:01:41 |
VIVIT | Do you mean "for each set there exists some prime number of which all members of that set are a multiple"? | 22:03:10 |
Cur_固嚛訥 | they collectively factor into the same set of primes. | 22:04:32 |
Cur_固嚛訥 | {2, 2, 2, 3, 3, 5} | 22:04:59 |
VIVIT | You can't factor into a set. | 22:05:00 |
VIVIT | You can factor into each member of a set, but not into the set itself. | 22:05:13 |
VIVIT | Also you can't factor into a prime (unless you are either 1 or that prime). | 22:05:53 |
Cur_固嚛訥 | No, you factor into primes. Every number is merely a representation of its prime factors. | 22:06:40 |